The Red Devils are resigned to losing Pogba this summer if Real Madrid can come close to their asking price of nearly 150 million.
United understand they may be powerless to stop Pogba if he hands in a transfer request.
And in that event, they would go after Saul from Atletico as their main central midfield target, according to Spanish outlet AS - cited by Sports Witness.
United are also linked with Bruno Fernandes from Sporting, but that transfer is seen as independent of the Pogba saga.
The 24-year-old Saul would be a tricky singing, as United may have to pay his buyout clause of £134.5 million if they want to buy him.